Question: Solve for $x$ and $y$ using elimination. ${-3x-y = -21}$ ${5x+y = 33}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $2x = 12$ $\dfrac{2x}{{2}} = \dfrac{12}{{2}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-3x-y = -21}\thinspace$ to find $y$ ${-3}{(6)}{ - y = -21}$ $-18-y = -21$ $-18{+18} - y = -21{+18}$ $-y = -3$ $\dfrac{-y}{{-1}} = \dfrac{-3}{{-1}}$ ${y = 3}$ You can also plug ${x = 6}$ into $\thinspace {5x+y = 33}\thinspace$ and get the same answer for $y$ : ${5}{(6)}{ + y = 33}$ ${y = 3}$